DAIB
Unless your surname is Yeager, I can advise you that the most you may see of an aircraft at 60nm distance is the contrail, or possibly if the sun is in the right position, you may see a glint off the aircraft. In reality, you need to be at less than 30nm to discern the shape. Often, even with TCAS, if approaching head on, you won't see the target until inside 20nm, quite often 10nm.
Rest assured that this aircraft would have been at a different altitude. Even as an experienced airline pilot, I find it difficult at distance to judge relative altitudes - often something I think is above turns out to be below. From the cabin through a side window you haven't got a cat in hells chance of quantifying anything.
About 4 years ago I had a note passed forward from a PPL holder sat down the back claiming that we had had a near miss (hate that term!) over northern Europe and that he had witnessed it. He gave me his mobiloe phone number, and I seriously believed that he was likely to contact the press, so I phoned our Media Comms group to forewarn them. Nothing resulted, not was there any abnormal incident during the flight.